A345161 - OEIS

A345161

If n = Product (p_j^k_j) then a(n) = max (nextprime(p_j) - p_j), where nextprime = A151800.

1, 1, 2, 1, 2, 2, 4, 1, 2, 2, 2, 2, 4, 4, 2, 1, 2, 2, 4, 2, 4, 2, 6, 2, 2, 4, 2, 4, 2, 2, 6, 1, 2, 2, 4, 2, 4, 4, 4, 2, 2, 4, 4, 2, 2, 6, 6, 2, 4, 2, 2, 4, 6, 2, 2, 4, 4, 2, 2, 2, 6, 6, 4, 1, 4, 2, 4, 2, 6, 4, 2, 2, 6, 4, 2, 4, 4, 4, 4, 2, 2, 2, 6, 4, 2, 4, 2, 2, 8, 2

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OFFSET

1,3

LINKS

Table of n, a(n) for n=1..90.

Ilya Gutkovskiy, Plot of (1/prime(n)) * Sum_{k=1..n} a(k)

Index entries for sequences computed from indices in prime factorization

Index entries for primes, gaps between

FORMULA

If n = Product (p_j^k_j) then a(n) = max (prime(pi(p_j) + 1) - p_j), where pi = A000720.

a(2^j*n) = a(n).

a(n^j) = a(n), j > 0.